Like Bombardier, I'm questioning your ability of being accepted by any branch, given your medical history. Like someone else suggested, I'd talk to a recruiter or two about their minimum requirements. I don't know anything about your asthma, but I do know that people can grow out of it during their adolesence.
I wouldn't worry too much about your physical strength. You're still a growing lad with a couple more years, minimum, to fully develope. However, be advised that ALL branches have a Basic Training program that requires a certain amount of physical fitness; some more than others. Plus, the military has a way of slimming down or bulking up recruits as needed through physical exercise and diet. Myself [I turned 19 in Basic], I was 5'11" and 155lbs. when I entered the Army. When I graduated from Jump School 6mos. later, I was 6'0" and 175lbs..
I voted for the Air Force as my suggestion, given your quest for a tech job. Plus, their living conditions and food is better than the Army [I know this firsthand] and Marines. I think the Navy lives pretty good, too.
Good luck at whatever choice you make.
P.S. You DO know that none of us can actually pick this for you. It ultimately is your decision based on what you want out of it and feel that you can put into it.
